Interpretation of Raman spectra of disordered and amorphous carbon

The model and theoretical understanding of the Raman spectra in disordered and amorphous carbon are given. The nature of the G and D vibration modes in graphite is analyzed in terms of the resonant excitation of \ensuremath{\pi} states and the long-range polarizability of \ensuremath{\pi} bonding. Visible Raman data on disordered, amorphous, and diamondlike carbon are classified in a three-stage model to show the factors that control the position, intensity, and widths of the G and D peaks. It is shown that the visible Raman spectra depend formally on the configuration of the ${\mathrm{sp}}^{2}$ sites in ${\mathrm{sp}}^{2}$-bonded clusters. In cases where the ${\mathrm{sp}}^{2}$ clustering is controlled by the ${\mathrm{sp}}^{3}$ fraction, such as in as-deposited tetrahedral amorphous carbon (ta-C) or hydrogenated amorphous carbon (a-C:H) films, the visible Raman parameters can be used to derive the ${\mathrm{sp}}^{3}$ fraction.